A221455 Number of 0..4 arrays of length n with each element unequal to at least one neighbor, with new values introduced in 0..4 order.

0, 1, 2, 7, 25, 101, 436, 1971, 9159, 43262, 206285, 988963, 4755888, 22910979, 110480787, 533057462, 2572761417, 12419474751, 59958562568, 289483787719, 1397691920591, 6748491159958, 32584154032229, 157329000870907

Offset

1,3

Comments

Column 4 of A221459.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 7*a(n-1) - 7*a(n-2) - 20*a(n-3) + 10*a(n-4) + 24*a(n-5) + 8*a(n-6).

Empirical g.f.: x^2*(1 - 5*x + 10*x^3 + 5*x^4) / ((1 - x - x^2)*(1 - 2*x - 2*x^2)*(1 - 4*x - 4*x^2)). - Colin Barker, Aug 05 2018

Example

Some solutions for n=6:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....1....1....1....1....1....1....1....1....1....1....1....1....1
..1....2....0....0....2....2....2....2....2....2....2....0....2....0....1....2
..0....1....2....2....1....3....2....1....0....3....0....0....3....2....2....0
..1....1....2....3....3....4....3....3....1....0....3....2....2....2....3....3
..0....2....3....1....2....0....4....0....0....2....2....1....1....0....2....1

Crossrefs

Cf. A221459.

Sequence in context: A150498 A150499 A150500 * A150501 A150502 A150503

Adjacent sequences: A221452 A221453 A221454 * A221456 A221457 A221458

Keyword

nonn

Author

R. H. Hardin, Jan 17 2013

Status

approved